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Lecture 6 Notes

# 1111 a 1110 b 1011 1111 1121 0 or l

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Unformatted text preview: o p electrons Summary so far: L=2, M=2,1,0,-1,-2 (11)22 = 11,11 1 { 10,11 + 11,10 } 2 1 (11)20 = { 1 − 1,11 + 2 10,10 + 11,1 − 1 } 6 1 (11)2 − 1 = { 10,1 − 1 + 1 − 1,10 } 2 (11)2 − 2 = 1 − 1,1 − 1 (11)21 = / Example: two p electrons Next step: L=1, M=1 ! "# \$ %& (11)11 = a 11,10 + b 10,11 (11)11 (11)21 = 0 or L+ (11)11 = 0 5 a+b = 0 * (11)11 = a 11,10 + b 10,11 Maximum m1 a is positive Example: two p electrons Next step: L=1, M=1,0,-1 (11)11 = a 11,10 − a 10,11 6 (11)11 = - . a (11)11 (11)11 = 1 → a = 1 2 1 { 11,10 − 10,11 } 2 ' \$ 1 { 11,1 − 1 − 1 − 1,11 } 2 1 (11)1 − 1 = { 10,1 − 1 − 1 − 1,10 } 2 (11)10 = 4 Example: two p electrons Next step: L=0, M=0 - . ! #- .&&% (11)00 = a 10,10 + b 1 − 1,11 + c 11,1 − 1 (11)10 (11)00 = 0 → b = c (11)20 (11)00 = 0 → a = −b Phase convention : c must be positive. (11)00 = −a 10,10 + a 1 − 1,11 + a 11,1 − 1 6 (11)00 = a (11)00 (11)00 = 1 → a = 1 3 1 { 1 − 1,11 − 10,10 + 11,1 − 1 } 3 Note: we also calculated all relevant Note: Clebsch-Gordon coefficients C...
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